Lol so Easy.
Oviously is Lucy (nyu) from Elfen Lied.
She never had parents, or anything like it. She was ever hated and satirized at school, she only once had a good time,
with Kouta that lied to her, then she found him with his cousing (girl) hugging in front of her...
The worst part. Her first friend (she only had 2 friends) was a dog, who was killed in front of her by less miserable kids of her "school".
Now thats a bad childhood.